Towards a realistic model of cortical dynamics at criticality

Idling brain: A computationally powerful regime

A significant portion of communication between neurons in the mammalian brain is mediated by bursts of electrical pulses that propagate from neuron to neuron via chemical synapses. These pulses are called action potentials or spikes. Just as knowledge of collective properties of feathers making up bird wings can illuminate the study of avian flight, elucidating collective dynamics of neuronal populations can advance our understanding of how large networks of neurons can give rise to behavior and cognition.
My research focuses on spontaneous dynamics of neuronal networks and its implications on the brain’s power to process information. The spontaneous network state is analogous to a daydreaming/idling brain where the network is free to explore the space that its dynamics allow. There is no external drive stimulating the network. Once given an initial kick, the network can subsequently maintain its own activity without further external support.

Towards a realistic model of cortical dynamics at criticality

Idling brain: A computationally powerful regime

A significant portion of communication between neurons in the mammalian brain is mediated by bursts of electrical pulses that propagate from neuron to neuron via chemical synapses. These pulses are called action potentials or spikes. Just as knowledge of collective properties of feathers making up bird wings can illuminate the study of avian flight, elucidating collective dynamics of neuronal populations can advance our understanding of how large networks of neurons can give rise to behavior and cognition.
My research focuses on spontaneous dynamics of neuronal networks and its implications on the brain’s power to process information. The spontaneous network state is analogous to a daydreaming/idling brain where the network is free to explore the space that its dynamics allow. There is no external drive stimulating the network. Once given an initial kick, the network can subsequently maintain its own activity without further external support.

From the standpoint of information capacity, entropy of spontaneous activity can be estimated to determine the repertoire of activity patterns available for a network to exploit for learning and encoding information. Deviations from criticality in neuronal tissues and simulation have been known to produce lower levels of entropy/information capacity.

From the perspective of information propagation among neurons, one can stimulate a selected number of neurons in one area and observe if the stimulation triggers stereotypical patterns across trials in areas that are downstream of the stimulated neurons. A subcritical network would fail to propagate the stimulation-induced signal consistently and remain close to a baseline level of activation. A supercritical network would produce a large cascade of random epileptic activity in downstream/output neurons. Only a critically balanced network would be able to transmit signal patterns robustly in a replicable fashion. Mappings between inputs and outputs should be most reliable at the critical point. The information theoretic metric of mutual information can be used to assess how much information of input activity is encoded in downstream/output activity.

While the aforementioned procedures do not explicitly involve behavior, information theoretic metrics are very generic. One can build networks that perform certain tasks, simultaneously characterize inputs to the networks, network activation patterns during task performance, and the networks’ behavior in completing the tasks. Subsequent analysis of information flow can then inform us of the significance of critical dynamics in a behaviorally relevant context.

Can you give some cognitive and/or behavior examples of the features you describe in your poster (at least as illustrative examples). Specifically can you provide a couple examples each for (1) spontaneous activity, (2) excitation-inhibition balance, (3) critical dynamics i.e. the avalanche, and (4) asynchronous irregular dynammics.

To clarify, I am only asking you to come up with some hypothetical examples to illustrate these concepts.

I certainly can. The former two concepts have clearer mappings to cognitive/behavioral analogues than the latter two. In any case, the following should clarify each and indicate how they are related to each other.

a) Spontaneous activity corresponds to the state where the brain is freely exploring various patterns. This is the idling/daydreaming state, where patterns/thoughts within the brain are intrinsically generated with minimal sensory inputs.

b) If excitation is stronger than inhibition, the brain is overly active and can enter an epileptic state. This is intimately related to synchronous regular dynamics, where neurons are firing with high level of simultaneity. The strong entrainment creates a highly ordered state and the brain enters a seizure and loses the ability to process information.

If inhibition is stronger than excitation, neuronal activity dissipates quickly and fails to propagate from one neuron to the next. This would be detrimental to integration of information across brain regions. This is a brain-dead/staring-into-the-void sort of state. This also leads to an inability to process information.

c) Critical dynamics, as characterized by avalanche statistics, can emerge only when excitation and inhibition are balanced. On average, under such a state, the firing of one neuron will trigger the firing of exactly one other neuron. There will be no runaway excitation or overdamping from inhibition. In principle, critical dynamics can be driven by external inputs from the peripheral sensory organs or internally generated as spontaneous activity. Some researchers have hypothesized that critical dynamics are characteristic of a healthy adult brain. Significant deviation from criticality could lead to pathological mental states.

d) Asynchronous irregular dynamics are simply the dynamics observed under the spontaneous/idling state. This type of dynamics means that neurons in the network would not collectively induce an epileptic state. In addition, the network is sensitive to external sensory inputs so that it can effectively distinguish between different signals. This ability is of course essential to survival.

I would like to take this opportunity to emphasize that although the study of collective dynamics of neurons is fundamentally abstract and challenging to convey, it is absolutely central to understanding how the brain gives rise to the mind and behavior. I endeavor to do my best to make the ideas more concrete and relevant. I hope I have duly addressed your questions. Do not hesitate to let me know if you have any further questions. I would gladly respond to them!

Intriguing. While I don’t disagree that criticality may be a central feature of neural systems, it is not clear how simulating a network with certain connection densities and strengths will teach us about actual brains unless we have some empirical evidence that the simulated structure is similar to existing structures. Do you know specifically if the 80/20 split is realistic for the cortex, or elsewhere?

Regarding empirical evidence, I am using connection probabilities and strengths that are in fact of the same order found in experiments. Furthermore, my model uses the “adaptive exponential integrate-and-fire” neuron, which is by far the most realistic neuronal model that has been applied to examine critical dynamics. I have also taken into account delays in physical propagation of electrical signals between neurons, which have largely been overlooked. Hence, my model is far from being devoid of realism. In fact, I do my best to balance empirical data and parsimony. For even more detailed structure, the literature does not tell us enough about canonical circuits across the brain that would justify the creation of more refined models, for any models built on such region-specific information would risk being too narrow in its applicability. In the future, I can specialize my models to incorporate more region specific data. At the moment, distilling the essential behavior of a more generic form of empirically supported cortical structure is likely more illuminating.

Variation in the mix certainly exists depending on the specific region of interest. However, the 80/20 split is indeed realistic for the cortex. Researcher have also used 70/30, 75/25, and other mixes close to 80/20 for at least two decades. The dynamics of my model, like most models, do not hinge upon a narrow range of parameters. I can change the mix and yet retain the essential network behavior. The mean firing rate or coefficient of variation of neurons might differ slightly while the critical and asynchronous irregular activity remain intact.

I have two answers to your question. They are diametrically opposed in flavor. Let me elaborate on them in turn.

First, the study of cortical dynamics is fundamental; it provides us with insights into the common underlying principles that govern how the brain works. It is practical in the sense that it offers a theoretical framework upon which we can understand how networks of interacting elements behave. Not to be facetious or equivocating in using both “practical” and “theoretical” in the same sentence, when I say “practical”, I am saying that it is useful and is exactly what people do to frame and visualize collective dynamics.

Specifically, the study of criticality in the cortex contributes to our understanding of the physics of networks, which in itself is an active area of research. Network dynamics is of interest not only to neuroscientists, but also occupies the attention of numerous researchers studying telecommunications, social networks/organization, gene regulation, species interaction, transportation, interactions between economic agents, etc. Understanding the core principles of cortical dynamics can lead to advancement in these areas and vice versa. Criticality and its associated power laws are very prevalent in nature. No overarching theory exists that can satisfactorily explain such prevalence. Cortical dynamics might have something to tell us about the generic behavior of networks.

So far, I have talked about potentially generalizable insights that criticality in the brain can offer. Instead of zooming out to envision general implications, let us zoom in and specialize towards practical applications. This is the second half of the response.

From the standpoint of clinical application, having a clear understanding of the role of criticality in the brain can lead to sophisticated assessment of mental capacity and diagnoses of mental disorders. As I have mentioned in one of my earlier responses, deviation from criticality is indicative of an imbalance in information transmission, which can significantly constrain and degrade the brain’s ability to integrate and process externally/internally generated signals. Through monitoring the brain’s network state using brain-scanning technologies with sufficient spatial and temporal resolution, researchers can develop neurodynamical biomarkers that identify brain regions disrupted by, e.g., Alzheimer’s disease, learning disability, stroke, traumatic injuries, etc. Physicians can then apply these technologies to diagnose and monitor a patient’s progress to recovery and customize treatments whenever intervention is deemed appropriate.

From a machine learning and human-machine interface perspective, the study of critical dynamics can inspire more powerful machines and algorithms that are capable of performing tasks that humans find easy but have been difficult to replicate in existing machines. A solid understanding of cortical dynamics and the ability to track those dynamics in real-time can also give rise to more effectively tuned and responsive human-machine interfaces that are important for, e.g. neuroprosthetics.

could you please help me understand/articulate the added value your research provides to existing knowledge in this field? in what way do you think your contribution will change what we currently know (or think we know) about this topic?

The two questions are very much related and have significant overlaps. Let me address them in a single response.

First and foremost, in the immediate term, my research adds value to current knowledge in the field because it has a high degree of realism compared to existing models. Neuronal models that have been used to study criticality fall into two classes — those that fire probabilistically, which loosely speaking is based on flips of biased coins, and those that mimic membrane potential of neurons. While the latter class is more realistic than the former, a sole variant in this class that has been used extensively in the literature is overly simplistic and does not account for many important firing dynamics commonly found in biological neurons. Among the dynamical features that are unaccounted for include spike frequency adaptation, initial bursting of spikes, fast and slow tonic spiking, and smooth spike initiation.

Without going too far afield into the mathematics of single neuron models, the “adaptive exponential integrate-and-fire” (AdEx) model that is used in my simulations not only exhibits all the dynamical features that have just been mentioned, it has outperformed its more rudimentary cousin on multiple benchmark tests. The benchmarks are done by comparing spike sequences of the models against those of real biological neurons. The AdEx model yields matches of 60% to 100% under a resolution of 4ms while the more primitive model produces matches less than 50% of the time.

Other realistic features of my model include axonal delays, synaptic depression and facilitation, and temporal profiles of postsynaptic potentials. Most of these have not been incorporated into existing models of critical neuronal networks. The details of these features are not crucial in answering your question; I just want to demonstrate that I have made a substantial effort in grounding my model in observed characteristics of actual cortical neurons. This harkens back to the title of my poster.

The benefit of having realism is the ability to study and isolate the effect of changes in model behavior under different treatments. For example, if there is a high degree of synaptic depression due to a change in the intrinsic properties of neurons (perhaps from disease or a bad diet), one would expect a previously critical network would turn subcritical due to an overall dampening of signal propagation. This is analogous to having a mind that is lucid and receptive to sensory inputs to one that is clouded and obtuse. I hope this example is sufficiently concrete and illustrative. If it is not, please let me know and I will elaborate or conjure up an alternative scenario.

Secondly, further into the horizon, from my research in criticality in the brain, I hope to shed light on general network dynamics that are relevant for other fields, bridging any divisions wherever possible. This is a problem of generalization that I mentioned in the first half of my response to the last question. Of course, this is a more elusive but very important goal. At this point, it is my guess that this is where the greatest surprises will emerge.

Thank you, Philomena! Criticality itself is an inherently complex and expansive topic that requires a substantial amount of mathematical formalism to fully understand. With fewer than three minutes, the best I could do to convey it was to help the audience develop a little intuition for it through simple analogies. I am very glad that you liked the Rock and Hulk Hogan analogy!